Rational Exponents and Radicals

When we raise a number to $\frac{1}{2},$ it's the same as taking the square root of that number.

The expression $16^{\frac{1}{2}}$ is equal to 4.

Check with a calculator

We determine the value of the expression $16^{\frac{1}{2}}$ on our calculator by writing the number $16,$ then pressing $\boxed{\hat{}}$ and finally writing the fraction $\frac{1}{2}$ within parentheses. We finish by pressing $\boxed{\text{ENTER}}.$

Rewrite $27^{\frac{1}{3}}$ as $\sqrt[3]{27},$ which is the number which multiplied by itself three times gives 27. We know that $$27=3\cdot 3\cdot 3.$$ Therefore, $27^{\frac{1}{3}}$ is equal to $3.$

Check with a calculator

We can determine the value of the expression $27^{\frac{1}{3}}$ on our calculator by using the same method as in Part A.